At 12 o'clock on February 27, the 32nd issue of "Zhang Chaoyang's Physics Class" began broadcasting. Zhang Chaoyang, founder, chairman of the board and CEO of Sohu, sat in the live video broadcast room of Sohu. He first introduced the concepts of quasi-static processes and reversible processes, using the example of objects sliding off rough surfaces to illustrate the irreversibility of macroscopic energy dissipation to the irregular motion energy of microscopic particles. This is followed by an introduction to two typical and equivalent formulations of the second law of thermodynamics, which it uses to prove Carnot's theorem that the efficiency of any irreversible heat engine operating between the same high and low temperature heat sources cannot be greater than that of a reversible heat engine. Using the ideal gas as the operating medium of the Carnot heater, the relationship between the efficiency of the heat engine and the temperature can be calculated, and the concept of entropy can be introduced. Discussing the variation of entropy before and after the free expansion of an ideal gas, it is possible to relate the thermodynamic definition of entropy to the Boltzmann definition of entropy.
"Recently, many physicists have settled in Sohu Video, and this morning there is Zhou Siyi's 'String Theory World'." At the beginning, Zhang Chaoyang recommended other knowledge live lessons of Sohu Video to netizens, and reminded netizens, "The whole world is paying attention to Ukraine, and Sohu News is also reporting." We hid in small buildings and continued to learn. He introduced the focus of today's course, "We continue to study thermodynamics. ”
The second law of thermodynamics and its typical equivalent formulation
"For isolated systems or systems with constant external conditions, after a long enough time, the various macroscopic properties of the system no longer change with time, such a state is called thermodynamic equilibrium. If the external conditions in which the system is located changes, the interaction between the outside world and the system will change the state of the system, and at every moment in this process, the state of the system is infinitely close to the equilibrium state, and this process is called a quasi-static process. ”
Zhang Chaoyang started from the second law of thermodynamics. He explained that in general, as long as the external conditions change relatively slowly, the process of the system re-reaching equilibrium is very fast relative to the change of external conditions, and each instantaneous approximation is the equilibrium state, and this slow process can be considered a quasi-static process.
He went on to point out that equilibrium states can be described by state parameters, so that each moment of a quasi-static process can be described by a state parameter, and its process can correspond to a curve on the phase diagram. As for the non-quasi-static process, he gave the example of the free expansion of gases, using a separator to divide a container into two, filled with gas on one side and a vacuum on the other. The separator is removed and the gas expands rapidly, filling the entire container. Obviously, in this process, the gas density and pressure and other parameters distribution is uneven, not equilibrium state, and the gas fills the entire container, after reaching a new equilibrium, its macroscopic parameters will no longer change, that is, the gas will not spontaneously return to the state before the partition extraction, which shows that the non-equilibrium process is irreversible.
He further explained that a system starts from a certain state, passes through a certain process, reaches another state, and if there is another process, it can return the system to the original state, and at the same time eliminate all the effects of the original process on the outside world, then the original process is called a reversible process. He said, "The non-quasi-static process of the free expansion of gases is an irreversible process. In the absence of dissipation, quasi-static processes are reversible. ”
Zhang Chaoyang then uses an example of an object sliding down from a smooth surface to illustrate the concept of dissipation. If the surface is smooth, the kinetic energy of the object when it slides to the bottom is the gravitational potential energy at the initial moment. If the surface is not smooth, due to the friction between the object and the surface, when the object reaches the bottom, its kinetic energy will be less than the gravitational potential energy at the initial moment. The friction force is due to the molecular force on the surface and surface of the object, the loss of macroscopic ordered energy, through this force into the irregular thermal motion of molecules, the dissipation of this ordered energy to the irregular energy, is obviously irreversible.
"The second law of thermodynamics summarizes the various claims made about the irreversibility of various irreversible processes, and I introduce two typical but equivalent formulations." Zhang Chaoyang said that Clausius's expression means that it is impossible to transfer heat from low-temperature objects to high-temperature objects without causing other changes. The Kelvin formulation, on the other hand, states that it is impossible to absorb heat from a single heat source to completely become a useful function without causing other changes.
(Zhang Chaoyang introduced the second law of thermodynamics)
Kano's theorem: the heat source of high temperature and low temperature is determined, and the reversible heat machine has the highest efficiency
Previously, Zhang Chaoyang introduced the Carnot cycle, and he continued to study the efficiency of the heat engine working on the Carnot cycle. He said, "Each process of the Carnot cycle is a quasi-static process, a reversible process, and the heat machine that uses the Carnot cycle to absorb heat from a high-temperature heat source to do external work is a reversible heat machine." Carnot's theorem states that between the same high-temperature heat source and the same low-temperature heat source, the efficiency of all the irreversible heat engines working cannot be greater than that of reversible heat engines. Among them, the efficiency of the heat engine refers to the ratio of the useful work W done by the heat engine to the outside world and the heat Q it absorbs from the high temperature heat source:
"The second law of thermodynamics can be used to prove Carnot's theorem." Zhang Chaoyang went on to explain that first consider the two heat engines A and B, assuming that they both absorb heat from high-temperature heat sources with Q1, but the external work is W and W', then their efficiencies are:
He reminded netizens that assuming that the heat engine A is a reversible heat engine, if you want to use the disproof method to prove Carnot's theorem, you need to first assume that it is not true, that is, the energy of ηA0. At the end of the combined cycle, the working substances of the two heat engines are restored to their original state, and the high temperature heat source does not change, which is equivalent to the heat engine absorbing the heat of W'-W>0 from a single heat source to make it completely useful without causing other changes, which violates the Kelvin expression of the second law of thermodynamics. So the initial hypothesis is ηA
(Proof of Carnot's theorem using the second law of thermodynamics)
State function entropy: macroscopic expression from the efficiency of the heat engine, microscopic significance from the statistical number
Zhang Chaoyang further explained that assuming that the aforementioned thermal engine B is also a reversible heat machine like the heat engine A, then according to Carnot's theorem, ηA ≤ηB can be obtained, combined with the proven ηA≥ηB, ηA = ηB can be obtained. "This shows that reversible heat engines that operate between two heat sources of a certain temperature have equal efficiency." He reminded netizens, "This also shows that the efficiency of the reversible heat machine has nothing to do with the specific working substance, then the efficiency can only be determined by the heat source, and the most basic feature of the heat source is temperature, so the efficiency is only a function of temperature." "Assuming that the heat engine absorbs heat from the high-temperature heat source T1 and exothermics the low-temperature heat source T2 Q2, and the first law of thermodynamics knows that the useful function is Q1-Q2, then the heat engine efficiency can be written as:
And since efficiency is only a function of temperature, it can be obtained:
Next, Zhang Chaoyang used the ideal gas as the working substance of the heat engine as an example to derive the form of f. From his derivation, it can be seen that the process of absorbing heat from the high-temperature heat source T1 is a to b, and the volume expands from Va to Vb, which can be seen by the second law of thermodynamics, and the heat absorbed by a small process is Q=dU+pdV, and the previous lesson also knows that the internal energy is only a function of temperature T1, in this isothermal process dU=0, then the heat Q1 absorbed by the ideal gas from the high-temperature heat source is:
The process of heat release in contact between the ideal gas and the low-temperature heat source T2 is c to d in the figure, and the volume is reduced from Vc to Vd, and the same reason can be calculated that the heat released to the low-temperature heat source Q2 is:
In addition, since b to c and d to a are adiabatic expansions, the insulation equation derived from the previous lesson can be obtained:
Divide the above left equation by the equation on the right:
From the ideal gas state equation at each point of abcd, we can obtain:
Then the ideal gas state equation and the thermal equation above can be combined to obtain:
Using this conclusion, it can finally be determined that the ratio of Q2 to Q1 is related to temperature as follows:
(Calculation of the efficiency of the heat engine when the ideal gas is used as the working substance of the heat engine)
"It can be seen that the efficiency of the heat engine is indeed only related to the temperature of the two heat sources, and it is expressed in a very simple form of ratio using the Kelvin temperature." Zhang Chaoyang said while rewriting the formula as:
Zhang Chaoyang introduced the concept of entropy according to this formula. He explained that for any quasi-static process of the system, one of the tiny processes is selected, and the temperature in this tiny process is approximately unchanged, set to T, and in this process it absorbs the heat of Q. We can introduce an auxiliary heat source T'=1K and a Carnot heater, which treats the system as a heat source, works between the system and the auxiliary heat source of T'=1K, and requires the Carnot heater to release Q heat to the system with a temperature of T. The Carnot heat machine that meets this condition absorbs Q' heat from the auxiliary heat source, and Q/T= Q'/T'= Q'/1K can be obtained according to the relationship between the efficiency of the reversible heat machine and the temperature. For other small processes, a Carnot heater can also be introduced to work between the system and the auxiliary heat source. Note that the different Carnot heat engines here work on the same T'=1K auxiliary heat source, so that after accumulating into a finite large process, assuming that all Carnot heat machines absorb a total of Q' heat from the auxiliary heat source, the change in entropy of the corresponding system can be defined as S = Q'/T'= Q'/1K, because the temperature of the auxiliary heat source is 1K, and its entropy change value is equal to the total heat provided by this auxiliary heat source. If the system reaches state b through a quasi-static process from state a, entropy is expressed by the temperature of the system and the heat it absorbs, and entropy can also be written as:
(Zhang Chaoyang introduces the definition of entropy)
"Entropy is a state function that has nothing to do with thermal processes, only with the state of the system. Let's start with a simple example and get a feel for the concept of entropy. Zhang Chaoyang continued to deduce, considering the process of an ideal gas with a particle number of N freely expanding from volume Vi to volume Vf, this process is not a quasi-static process, so it cannot be directly applied to the above formula for entropy, but because entropy is a state function, its change is only determined by the initial state and terminal state of the gas, we can look for a quasi-static process to connect the initial and final states of the system, and we can use the above entropy calculation formula to calculate the change in entropy. In the process of free expansion, the ideal gas does not do work, the internal energy of the gas is unchanged, and the internal energy of the ideal gas is only related to the temperature, so the ideal gas temperature T of the initial and final states is unchanged, so that we can use the isothermal expansion process to connect the initial and final states of this free expansion. The expression of the heat absorbed by the ideal gas during isothermal expansion has been calculated earlier, and the change in entropy can be obtained by substituting it into the calculation formula of the above entropy as follows:
Netizens found from his deduction that when the volume of the container expands from Vi to Vf, the desirable position space of each particle in the ideal gas becomes larger than the original Vf/Vi, intuitively, equivalent to the number of desirable states of each particle Ω, and also becomes larger than the original Vf/Vi. Since the ideal gas is a near-independent particle system, the number of the entire ideal gas state with N particles will be greater than the original (Vf/Vi)^N times. If the number of gas states in the initial and final states is Ωi and Ωf, respectively, then there are:
This coincides with Boltzmann's definition of entropy, S=k lnΩ. This also shows that entropy is a measure of the degree of confusion in a system, and that the definition of this form of entropy has great significance for subsequent statistical mechanics. Zhang Chaoyang pointed out the importance of the concept of entropy, adding, "Next week, we will have a broader discussion of the concept of entropy." ”
Build a knowledge live broadcast platform: Sohu video power value live broadcast to attract many popular science broadcasters to settle in
Up to now, "Zhang Chaoyang's Physics Class" has been broadcast live for more than 30 issues. Zhang Chaoyang first started with classical physics, popularized Newton's laws of motion and conservation of energy momentum, explained the equations of mechanical vibration and fluctuation and calculated the speed of sound in the air, and discussed the ideal gas state equation and the energy equal division theorem related to this. Later, starting from the "two dark clouds" of classical physics, the transition to modern physics includes a series of formulas such as Wien, Rayleigh-Kings, Stephan, and Planck derived from the study of blackbody radiation; relativistic issues caused by electromagnetism and the properties of space-time, such as the Lorentz transform, the slow clock of the ruler, the relationship between mass and energy, and particle decay.
Since then, it has gradually entered the field of quantum mechanics, from the basic theoretical content of Schrödinger equations, operator pairs and easy relations, uncertainty principles, etc., to basic models such as infinite deep potential wells, hydrogen atomic wave functions, atomic energy levels and degeneracy, and then to more specific and practical cases such as harmonic quantization, molecular vibrational rotation spectrum, freezing of degrees of freedom, and temperature ladders of gas specific heat. Rich in content and wide coverage, theoretical formulas from shallow to deep, complex and simple, the research objects from small to large, from less to more, from single-electron atoms to multi-electron atoms, polyatomic molecules, and then to the macroscopic matter composed of many particles, in fact, has gradually entered the field of statistical physics. The subsequent Boltzmann distribution, Maxwell's velocity distribution law, etc., are also introduced in the trend, which is logical.
From more than 30 physics lessons, it can be seen that the live broadcast style of "Zhang Chaoyang's Physics Class" is unique - by observing the phenomena of daily life, using topics that netizens are more familiar with to enhance interest, and then explaining the physical principles behind it in the way of formula derivation, "seeing the essence through the phenomenon", and then solving similar problems in life in turn.
Zhang Chaoyang believes that studying the natural world is a particularly interesting thing, and he hopes that the audience of physics classes can maintain curiosity, "driven by curiosity, understand the mysteries of nature and understand the truth of our survival in this world." The course is broadcast live on Sohu video every Friday and Sunday at 12:00. At the same time, netizens can search for "Zhang Chaoyang" in the Sohu video "Attention Stream" to watch the full video playback of previous periods.
In addition to "Zhang Chaoyang's Physics Class", Sohu Video also invites leading broadcasters in various professional fields to settle in, live broadcast popular science knowledge, and transmit value. Dr. Chen Zheng, a teacher at the School of Science of Beijing Jiaotong University, played a "strange scientific experiment" and walked into the "wave-particle duality of light"; Bao Kun, a doctor of physical chemistry at Cornell University, incarnated as "Bao Daren plays science" to teach ordinary people to understand the 2021 Nobel Prize; and Liu Boyang, a doctor of astrophysics, popularized "How is a total solar eclipse", and Zhou Siyi, a doctor of theoretical physics, also opened a live class on "String Theory World". In the future, more knowledge broadcasters will settle in and interact with science together.